Those who study classiication theory, whether it be in the form of statistical pattern recognition, syntactical pattern recognition, or neural approaches to classiication are aware of the recent achievements and advances of their elds. For example names such as Bayes, Fisher, Wald, Fu, and Rosenblatt are well known for their pioneering contributions to classiication theory. However, few are awa...

Bayesian analysis incorporates different sources of information into a single analysis through Bayes theorem. When one or more of the sources of information are suspect (e.g., if the model assumed for the information is viewed as quite possibly being significantly flawed), there can be a concern that Bayes theorem allows this suspect information to overly influence the other sources of informat...

We developed a new algorithm to retrieve properties of non-precipitating liquid water clouds from millimeter wave radar and Microwave Radiometer (MWR) data using Bayes’ theorem of conditional probability. Bayes’ theorem relates the inverse problem (retrieving cloud properties from remotesensing observations) to the forward problem (modeling remote-sensing observations given a set of cloud prope...

Reasonable rational information processing is important in people’s in everyday decision-making. A number of features affect how environmental messages are processed, including the presentation format and the reliability of the information source. One way to measure the importance assigned to the source reliability is to frame the question in terms of Bayes’ theorem (Hahn & Harris, 2009). In tw...

A drawing of a graph on a surface is independently even if every pair of nonadjacent edges in the drawing crosses an even number of times. The Z2-genus of a graph G is the minimum g such that G has an independently even drawing on the orientable surface of genus g. An unpublished result by Robertson and Seymour implies that for every t, every graph of sufficiently large genus contains as a mino...

1. Deriving Bayes' Theorem Bayes' theorem is a piece of mathematics. It is called a theorem because it is derivable from a simple definition in probability theory. As a piece of mathematics, it is not controversial. Bayesianism, on the other hand, is a controversial philosophical theory in epistemology. It proposes that the mathematics of probability theory can be put to work in explicating var...

a two-factor experiment with interaction between factors wherein observations follow an inverse gaussian model is considered. analysis of the experiment is approached via an empirical bayes procedure. the conjugate family of prior distributions is considered. bayes and empirical bayes estimators are derived. application of the procedure is illustrated on a data set, which has previously been an...

The problem of stabilizing a second-order delay system using classical proportional-integralderivative PID controller is considered. An extension of the Hermite-Biehler theorem, which is applicable to quasipolynomials, is used to seek the set of complete stabilizing PID parameters. The range of admissible proportional gains is determined in closed form. For each proportional gain, the stabilizi...

In a previous Letter [Borsanyi et al., Phys. Rev. Lett. 111, 252001 (2013)] we determined the isospin mass splittings of the baryon octet from a lattice calculation based on N_{f}=2+1 QCD simulations to which QED effects have been added in a partially quenched setup. Using the same data we determine here the corrections to Dashen's theorem and the individual up and down quark masses. Our ensemb...